let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

Abstract. Let Mn;m be the set of n-by-m matrices with entries inthe field of real numbers. A matrix R in Mn = Mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if Re e, where e = (1; 1; : : : ; 1)t. For X; Y 2 Mn;m, X is said to besgut-majorized by Y (denoted by X sgut Y ) if there exists ann-by-n upper triangular g-row substochastic matrix R such thatX = RY . This ...

For two bipartite graphs G and G , a bijection ψ : E(G) → E(G) is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if ψ(M) is a perfect matching in G. We characterize bipartite graphs G and G which are related by a matching preserver and the matching preservers between them.

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.

A matrix R is said to be g-row substochastic if Re ≤ e. For X, Y ∈ Mn,m, it is said that X is sglt-majorized by Y , X ≺sglt Y , if there exists an n-by-n lower triangular g-row substochastic matrix R such that X = RY . This paper characterizes all (strong) linear preservers and strong linear preservers of ≺sglt on Rn and Mn,m, respectively.

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got use...